Screw Theory

We propose a minimal, testable theory for when geometry emerges from pregeometric tension in meaning—framing the transition as an observable event rather than a modeling assumption. We formalize the Span layer as the interference/condensation zone where folds, tension, and resonance accumulate into neighborhoods that prepare a spectrum; Span ends only when an onset triplet co-occurs: a rise in spectral gap (Δλ₂ ≥ ε), an intrinsic-dimension knee, and zigzag-persistence consolidation. On this basis we state six Emergence Conditions (E1–E6): local enabling (non-degenerate tension and directional fold-causality; resonance density; order-faithful composability; tension regularity), a global Cheeger floor for conductance, and the measurable onset triplet that licenses geometry. Together they yield a concise Geo-Bridge—P→Fold⁡σG→Spec(L,λ2,Ek)→Fisher(M,gV)\mathcal P \xrightarrow{\operatorname{Fold}_\sigma} G \xrightarrow{\text{Spec}} (L,\lambda_2,E_k) \xrightarrow{\text{Fisher}} (\mathcal M,g_V)—and delimit the post-onset window where the unique linear, local, reciprocal closure holds: B=σ∇gVSB=\sigma\nabla_{g_V}S. We corroborate the framework with Span mini-experiments: (I) resonance toggles advance onset and increase integrability, (II) Cheeger bottlenecks delay onset and destabilize topology, and (III) regularity breaks produce ill-conditioned Fisher charts despite spurious spectral hints. The work integrates an evidence-before-output gate (S⁵OS) and a reproducibility kit (seeds, thresholds, DOI’d artifacts), and clarifies minimal vs. sufficient conditions, nonlinear pre-onset dynamics, and cross-model/domain robustness for emergent discourse geometry.

This paper presents a systematic constraint-based analysis of the motion attributes of six parallel kinematic articulated wrist mechanisms from the existing literature. These motion attributes include the number, nature (i.e. pure rotation, or translation, or a combination), and location of mechanism’s Degrees of Freedom (DoFs) in the nominal and displaced configurations, range of operation along these DoFs, load transmission capability along these DoFs, and load bearing capability along the constraint directions. This systematic analysis reveals performance tradeoffs between these motion attributes for a given mechanism, as well as design tradeoffs across these multiple mechanisms with respect to these motion attributes. This analysis should help inform the suitability of a given mechanism for specific applications.

Currently, the cold-formed Steel sections (CFS) are increasingly used in light and mid-height buildings. So, this research examined the axial compression behavior of CFS thin-walled Zee-shaped section under pure axial monotonic loading. This study conducted full-scale tests on three specimens to investigate the three main modes of failure: local buckling, distortion buckling, and global buckling modes. The specimens were selected from CFS Zee sections with 600mm, 1000mm, and 2500mm. The imperfection of the CFS sections was captured by the 3D scanning before testing and implementation in the FE models. Then, the pure axial load was applied monotonic. The failure modes and axial capacity are discussed in detail. In addition, this research investigated the axial load-displacement responses and the axial load capacity. The energy dissipation with strength degradation was thoroughly investigated. A Finite Element Model (FEM) was conducted and verified by the experimental results. Finally, the FEM analysis was extended to study the behavior of the Zee section with a different range of dimensions to predict the section parameters' behavior under axial monotonic load.

An experimental study was performed to investigate the ultimate strength and modes of failure of axially loaded channel rack columns with rear flanges. A total of 16 column specimens fabricated by press-brake forming method were tested up to failure. The material properties of the column specimens were determined using standard tensile coupon tests. The deformation and stress behavior of the tested columns were monitored using displacement transducers and strain gauges. The effects of column slenderness ratio, thickness, perforation, and end conditions on the column ultimate strength and mode of failure were studied. The test failure loads were compared to the ultimate load predictions of the 2001 AISI North American Specification. The comparison showed that the AISI procedure overestimates the failure load, which suggests that the proportioning of the cross-sectional dimensions of the lipped channel sections with rear flanges has a direct effect on the capacity of the columns.

This paper deals with finding the relation between modal natural frequencies change due to crack in shaft with respective crack depth and location. In this study we investigate relation among crack depth, crack location & natural frequency. Finite Element Analysis is done for single crack at different depth and crack thickness. The analysis results reveal, how modal natural frequencies decrease with change in crack size. It is known that when a shaft or structure suffers from crack or any damage then its dynamic property changes. The reason for this behaviour because of crack causes a stiffness reduction with an inherent reduction in modal natural frequencies which leads to the change in the dynamic response of the Shaft. Creo software is used for parametric modeling of Rotor Shaft as well as for static and dynamic analysis. Modal natural frequency was found to be decreasing with increase in crack depth and its width. This is new technology in Creo, so this study the FEA analysis is...

This paper deals with the singular configurations of symmetric 5-DOF parallel mechanisms performing three translational and two independent rotational DOFs. The screw theory approach is adopted in order to obtain the Jacobian matrices. The regularity of these matrices is examined using Grassmann-Cayley algebra and Grassmann geometry. More emphasis is placed on the geometric investigation of singular configurations by means of Grassmann-Cayley Algebra for a class of simplified designs whereas Grassmann geometry is used for a matter of comparison. The results provide algebraic expressions for the singularity conditions, in terms of some bracket monomials obtained from the superbracket decomposition. Accordingly, all the singularity conditions can be enumerated.

This paper extends a recently proposed singularity analysis method to lower-mobility parallel manipulators having an articulated nacelle. Using screw theory, a twist graph is introduced in order to simplify the constraint analysis of such manipulators. Then, a wrench graph is obtained in order to represent some points at infinity on the Plücker lines of the Jacobian matrix. Using Grassmann-Cayley algebra, the rank deficiency of the Jacobian matrix amounts to the vanishing condition of the superbracket. Accordingly, the parallel singularities are expressed in three different forms involving superbrackets, meet and join operators, and vector cross and dot products, respectively. The approach is explained through the singularity analysis of the H4 robot. All the singularity conditions of this robot are enumerated and the motions associated with these singularities are characterized.

The subject of this paper is about the conceptual design of parallel Schoenflies motion generators based on the wrench graph. By using screw theory and Grassmann geometry, some conditions on both the constraint and the actuation wrench systems are generated for the assembly of limbs of parallel Schoenflies motion generators, i.e., 3T1R parallel manipulators. Those conditions are somehow related to the kinematic singularities of the manipulators. Indeed, the parallel manipulator should not be in a constraint singularity in the starting configuration for a valid architecture, otherwise it cannot perform the required motion pattern. After satisfying the latter condition, the parallel manipulator should not be in an actuation singularity in a general configuration, otherwise the obtained parallel manipulator is permanently singular. Based on the assembly conditions, six types of wrench graphs are identified and correspond to six typical classes of 3T1R parallel manipulators. The geometric properties of these six classes are highlighted. A simplified expression of the superbracket decomposition is obtained for each class, which allows the determination and the comparison of the singularities of 3T1R parallel manipulators at their conceptual design stage. The methodology also provides new architectures of parallel Schoenflies motion generators based on the classification of wrench graphs and on their singularity conditions.

In the present study, the kinematics of a class of parallel manipulators with two translational and one rotational degrees-offreedom are addressed through the analysis of HALF robot. A detailed kinematic and constraint analysis of the robot is conducted. In addition, an exhaustive singularity characterization is presented with interpretation of the robot's behavior in singular poses. The implications of this study will initiate further investigations on the design of parallel manipulators belonging to the class of manipulators under consideration.

This paper presents a generic approach to analyze the singularity of robots with an articulated nacelle like the H4 robot. Using screw theory, the concept of equivalent twist graph is introduced in order to characterize the constraint wrenches and the actuation wrenches applied to the moving platform. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six Plücker vectors of finite and infinite lines in the projective space P 3 are reformulated in the superbracket decomposition in order to characterize geometrically the parallel singularities of the robot.

The paper presents a systematic non-iterative procedure for a priory design of link shapes for interference-free motion of a planar mechanism. We define the notions of unilayer and multi-layer links and show that generality of shapes that can be conceived depends upon the designer's choice about the physical implementation of the joints. We propose a matrix-based procedure for the determination of the nature of interaction among the links and joints during motion where each link can be multi-layer. Techniques for geometric synthesis as in the case of unilayer links could then be used by processing one layer at a time. The concept is demonstrated for the geometric synthesis of a six-bar Stephenson mechanism with one multi-layer link. A theory of simultaneous synthesis, using the concept of compliant motion, is also presented which does not have the limitations of order dependence inherently present in sweep-based methods.

The continuous development of the oil-manufacturing industries causes the necessity of improving extraction technologies. In this case, the specific interest is focused on the control systems of screw presses. Among a great variety of such machines, the small household presses are in significant demand among consumers. Various seeds and kernels require different technological conditions to be provided in order to maximize the qualitative and quantitative characteristics of the extracted oil. Therefore, the main objective of this research is developing and testing the control system allowing for automation of the oil extraction process. Particularly, the temperature parameters of the pressing chamber, extracted oil, and electric motor are to be monitored and limited. In addition, the consumer should be able to predefine the mass of the oil to be extracted. Considering the small household screw press LiangTai LTP200, the general algorithm (block diagram) of the control system operation is proposed and the corresponding experimental prototype is developed. The latter is based on the Arduino Mega microcontroller and is equipped with three temperature sensors, two coolers (fans), one heater, and one mass sensor. The proposed control system allows for continuous monitoring and limiting of the pressing chamber, oil, and electric motor temperatures, as well as the mass of the extracted oil. The experimental data show that the pressing chamber preheating process lasts for about 3 min (170…190 s) and its maximal temperature does not exceed 44°C. The temperature of the extracted oil does not rise over 61°C. The motor temperature changes within the range of 69...71°C. The oil extraction productivity is as follows: 1.2 kg/h (sunflower seeds), 1.06 kg/h (walnut kernels), 0.9 kg/h (almond kernels), and 0.78 kg/h (peanut kernels). The obtained results can used in further investigations focused on analyzing the influence of these parameters on the quantitative and qualitative characteristics of the extracted oil.

Indexing cam mechanism is one of most important mechanisms in automated machineries. This paper presents a general frame for kinematic analysis and geometry design of indexing cam mechanism, such as parallel cam mechanism and roller gear cam mechanism. This method applied screw theory to describe structure of cam mechanism and developed the kinematic equations by using Product of Exponentials Formula (PEF). As long as such structure parameters are given as position and orientation of central line in turret, cam and rollers, geometry modeling of indexing cam can be implemented in a general frame of kinematic equations by applying this method. The paper gives examples to obtain the geometry models of roller gear cam, barrel indexing cam and parallel indexing cam. Our work suggests that this method can avoid the burdensome work on building coordinate systems, transformation matrix and understanding on the mechanism. Moreover, this method can be used to innovate and design new types of indexing mechanism.

Variable-DOF (or kinematotropic) mechanisms are a class of reconfigurable mechanisms that have varying degrees of freedom (DOF) in different motion modes and can be reconfigured without disassembly. However, the number of proposed variable-DOF multi-loop planar mechanisms is currently limited. This paper introduces a new 8-link variable-DOF planar mechanism that has five motion modes. Firstly, the 8-link variable-DOF planar mechanism is described. Then, reconfiguration analysis of the mechanism is performed using a hybrid approach that combines elimination and computer algebraic geometry methods. The analysis reveals that the 8-link mechanism has one 2-DOF motion mode and four 1-DOF motion modes. It can switch among three motion modes at four transition configurations and between two motion modes at the remaining four transition configurations. The paper also highlights the geometric characteristics of the mechanism in different motion modes. In contrast to variable-DOF planar mecha...

This paper deals with the reconfiguration analysis of a 4-DOF (degrees-of-freedom) 3-RER parallel manipulator (PM) with equilateral triangular base and moving platform (ETBP), which is a special case of a 4-DOF PM in the literature. The 4-DOF 3-RER PM is composed of a base and a moving platform connected by three 3-RER legs, each of which is a serial kinematic chain composed of a revolute (R) joint, a planar (E) joint and an R joint in sequence. At first, a set of constraint equations of the 3-RER PM with ETBP is derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler-Rodrigues quaternion) and then solved in closed form. It is found that the 3-RER PM with ETBP has three 4-DOF operation modes if both the base and moving platform are identical or two 4-DOF operation modes if the base and moving platform are not identical. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the author of this paper. The transition configurations among different operation modes are also identified.

This article presents an asymmetric parallel manipulator with 2(RRPaRR)-PRRR kinematic chains. This manipulator aims to operate as a lower-mobility parallel manipulator with the pure translational motion of its platform. Therefore, a series of analyses are performed to fulfill this intention. First, the mobility analysis is performed by applying the Grübler-Kutzbach equation and the screw theory. Then, the kinematic, singularity, and workspace analysis are applied to analyze this PM. As a result, the application of the screw theory for the configuration of its kinematic chains shows its mobility in a pure translational motion in space. Then, this manipulator has a closed-form solution for its direct kinematic problem expressed in a quadratic equation. By applying singularity and workspace analysis via visualization, the singularity-free workspace along the z-axis of its workspace can be identified. This can later be used as a useful workspace. Overall, the presented manipulator can ...

Hoop truss deployable antenna can realize the communication and data transmission between satellite and earth, which is an important type of satellite antennas, and its configuration design is currently one of the research hotspots in the field of aerospace. Based on screw theory, configuration synthesis of the hoop truss deployable mechanisms for space antenna is studied in this paper. First, the constraint synthesis method based on screw theory is briefly described, the structure and folding principle of hoop truss deployable mechanism are analyzed. Then, structure decomposition of the hoop truss deployable mechanism is carried out, it is divided into upper hoop edge, lower hoop edge and connected rods. The movement features of the nodes are described by the prismatic (P) joints, configuration synthesis of the hoop edge mechanisms is carried out, and 18 kinds of constrained branch mechanisms are obtained, two kinds of constrained branch mechanisms are selected through analysis and optimization. Furthermore, hoop edge mechanisms are obtained by combining the constrained branch mechanisms, and five hoop truss deployable mechanisms are obtained through different connection combinations. Finally, simulation models of the five kinds of hoop truss deployable mechanism are built in Solidworks and Matlab software, the deployment processes are simulated and verified, and their characteristics are analyzed and discussed. The research in this paper provides a good reference for the configuration synthesis of spatial deployable mechanisms, and the hoop truss mechanisms obtained in this paper can be well applied in the field of aerospace.

Large diameter space deployable antenna is the key equipment for communication and data transmission between spacecraft and base stations on earth. Based on the overconstrained scissors mechanism, a double-hoop truss deployable antenna mechanism is constructed in this paper, which can be used as the antenna support mechanism for satellites and other spacecraft, and its kinematic characteristics and dynamics are analyzed based on screw theory. First, the configuration and the overconstrained features of the double-hoop truss deployable mechanism are analyzed with the truss mechanism divided into a plurality of mechanism units. The geometric conditions for the double-hoop form are also investigated with the consideration of joint size effects. Then, based on the screw theory, the degree of freedom (DOF) of the mechanism is analyzed, showing that this mechanism has only one DOF. Next, the velocity and acceleration of the components in the mechanism are examined. Through the screw and screw derivatives operation, the velocities and accelerations of the components and the Jacobian matrixes are obtained. Finally, a dynamic model of the double-hoop truss deployable mechanism is established based on the Newton-Euler equation and the principle of virtual work, and this model is verified by the numerical calculation and simulation verification. The overconstrained scissors double-hoop truss deployable antenna mechanism proposed in this paper has a good application prospect in the field of space deployable antennas, and the theoretical analysis method in this paper can provide insights into other complex spatial deployable mechanisms. INDEX TERMS Overconstrained mechanism, scissors mechanism, double-hoop truss deployable antenna, screw theory, kinematics, dynamics.

Large diameter space deployable antenna is the key equipment for communication and data transmission between spacecraft and base stations on earth. Based on the overconstrained scissors mechanism, a double-hoop truss deployable antenna mechanism is constructed in this paper, which can be used as the antenna support mechanism for satellites and other spacecraft, and its kinematic characteristics and dynamics are analyzed based on screw theory. First, the configuration and the overconstrained features of the double-hoop truss deployable mechanism are analyzed with the truss mechanism divided into a plurality of mechanism units. The geometric conditions for the double-hoop form are also investigated with the consideration of joint size effects. Then, based on the screw theory, the degree of freedom (DOF) of the mechanism is analyzed, showing that this mechanism has only one DOF. Next, the velocity and acceleration of the components in the mechanism are examined. Through the screw and screw derivatives operation, the velocities and accelerations of the components and the Jacobian matrixes are obtained. Finally, a dynamic model of the double-hoop truss deployable mechanism is established based on the Newton-Euler equation and the principle of virtual work, and this model is verified by the numerical calculation and simulation verification. The overconstrained scissors double-hoop truss deployable antenna mechanism proposed in this paper has a good application prospect in the field of space deployable antennas, and the theoretical analysis method in this paper can provide insights into other complex spatial deployable mechanisms. INDEX TERMS Overconstrained mechanism, scissors mechanism, double-hoop truss deployable antenna, screw theory, kinematics, dynamics.

Overconstrained mechanism has the advantages of large bearing capacity and high motion reliability, but its force analysis is complex and difficult because the mechanism system contains overconstraints. Considering the limb axial deformation, taking typical 2SS+P and 7-SS passive overconstrained mechanisms, 2SPS+P and 7-SPS active overconstrained mechanisms, and 2SPS+P and 7-SPS passive-input overconstrained mechanisms as examples, a new force analysis method based on the idea of equivalent stiffness is proposed. The equivalent stiffness matrix of passive overconstrained mechanism is derived by combining the force balance and deformation compatibility equations with consideration of axial elastic limb deformations. The relationship between the constraint wrench magnitudes and the external force, limb stiffness is established. The equivalent stiffness matrix of active overconstrained mechanism is derived by combining the force balance and displacement compatibility equations. Here, the relationship between the magnitudes of the actuated wrenches and the external force, limb stiffness is investigated. Combining with the equivalent stiffness of the passive overconstrained mechanism, an analytical relationship between the actuated forces of passive-input overconstrained mechanism and the output displacement, limb stiffness is explored. Finally, adaptability of the equivalent stiffness to overconstrained mechanisms is discussed, and the effect of the limb stiffness on overconstrained mechanisms force distribution is revealed. The research results provide a theoretical reference for the design, research and practical application of overconstrained mechanism.

The Kutzbach criterion, or the Gruebler's criterion, plays a significant role in the study of mechanism kinematics, specifically for determining the mobility of a mechanism. This paper provides an in-depth review of the Kutzbach criterion, its formulation, and practical applications in mechanical engineering, particularly in the analysis of planar and spatial mechanisms. A detailed discussion on its use in determining the degrees of freedom (DOF) in both simple and complex mechanisms is provided. The paper also explores the limitations of the criterion and suggests future directions for research.

Ancient Eleutherna, a city with a multinuclear organization, developed on and around the Nisi and Pyrgi hills, on the northwestern foothills of Psiloritis in Central Crete. On the central plateau of Pyrgi Hill, excavations by the University of Crete (Sector II-Central) revealed a cult building that functioned from the Archaic to Roman times, confirming that the acropolis of the ancient city was located there. At the center of the cella of the temple of the acropolis, an underground chamber was found, sealed by the Roman-paved floor. The upper part of the chamber consists of a cylindrical monolithic opening, within which a stone element and numerous stone fragments—carved from local limestone—were discovered. The painstaking process of joining the fragments largely restored a monolithic screw with a head diameter of 1.17 m, while the monolithic opening of the underground chamber was found to be its corresponding nut. This system secured the chamber by sealing it. The metal-lined deep holes found around the periphery of the nut were also attributed to the sealing/ securing system. This construction was identified as the thesauros of the temple, and according to excavation data, it dates back to the Hellenistic period. The article presents a detailed analysis of the screw-nut system, focusing on its geometry and the screwing method. Three-dimensional models of both the existing and restored forms of the system provide insight into this unique technological achievement, aiming to understand how it worked and its role within the ancient temple of the acropolis of Eleutherna.

A kinematic-structural analysis is considered on a well-known parallel kinematics manipulator: the Tsai manipulator, using procedures useful for other generic parallel manipulators. Firstly the kinematic analysis will be made, obtaining the singular configurations and the blocking positions, key points for the later structural analysis. Then the structural analysis of the mechanism will be made, observing the stiffness that presents for different positions within its workspace, and obtaining graphs that represent the stiffness of the mechanism based on the position.

The set of rigid displacements of the end-effector of a mechanism is ordinarily a manifold of the special Euclidean group SE(3). The tangent spaces of the manifold form vector spaces of twists describing the end-effector instantaneous motions. The twist space at any generic pose is often required to be a rigidly-displaced copy of the twist space in the home configuration: when this happens the twist space and the corresponding manifold are called persistent. There are three known families of persistent manifolds of SE(3). The first one comprises the Lie groups of SE(3), for which the twist space is invariant and coincides with a subalgebra of the Lie algebra of SE(3). The second family includes the symmetric spaces of SE(3), for which the twist space is a persistent Lie triple system. The third family is a subset of the product-of-exponential (POE) manifolds, which emerge by the product of two or more Lie groups and naturally describe the motion of serial chains. While the classification of Lie groups and symmetric spaces of SE(3) is state-of-the-art, the classification of persistent POE manifolds is yet to be completed. This paper provides the derivation and classification of persistent POE manifolds of dimension 3.

A system has been developed to interactively assemble modular and reconfigurable robotic systems in a computer animation environment. The modular robot is based on a set of one, two and three degree of freedom joint modules and generic links. These modules may be assembled into a large class of robotic systems that include serial, parallel, mobile and hybrid configurations. A model of the configured robotic system is immediately available for use in a wide variety of robotics research areas, including: obstacle avoidance, redundant inverse kinematics, dynamic simulations, mobile platforms and world model databases.

The utilization of cold-formed thin-walled members as structural members has gained significant popularity due to their advantages in fabrication, cost-effectiveness, and transportation convenience. However, the reduced thickness of the used sections poses challenges such as global, local, and distortional member buckling, leading to a decrease in their axial strength. This study focuses on addressing these challenges by connecting the channels together using screws as an alternative to welding, considering the cost, time, and ease of implementation. Conducting finite element analysis on structural columns built-up from cold-formed double C steel channels and subjected to axial loads, this paper verifies the numerical models used against experimental tests known from the literature. A comparison of experimental results with nonlinear FEA and AISI & AS/NZ standards reveals commendable agreement, particularly in predicting the buckling behavior of the built-up I-shaped CFS columns. While the results of the finite element analysis show an overestimation of approximately 3.6% compared to the experimental tests, the AISI and AS/NZS standards demonstrate a conservatism of about 3.0%. Furthermore, the current study investigates the influence of screw spacing on axial strength of built-up cold-formed steel columns. The findings are derived from 175 finite element experiments, evaluating seven different cross-sectional profiles with twelve distinct screw spacings. These spacings correspond to the half-wavelength of local, distortional, and global buckling, divided by values ranging from one to four. The screw spacing determined by half the local buckling half-wavelength along the webs’ centerline resulted in enhancements of 22%, 7%, 13%, and 11% in the critical elastic local, distortional, and global column buckling loads, as well as the nominal axial strength, respectively. These increases were even more pronounced for double-lane fasteners with the same spacing, yielding improvements of 25%, 46%, 17%, and 12%, respectively. For economic considerations, it is advisable to utilize single-lane fasteners with a half-wavelength equal to half the local buckling half-wavelength.

This paper presents the kinematics programming for Cooperative Robotic Systems (CRS), based on screw theory approach. It includes a systematic for modeling and programming robotic systems composed by any number of robots (not necessarily identical), working cooperatively to perform different tasks. In order to illustrate the application of the systematic, an example of CRS including four robots is presented. The kinematic computation of a CRS is made through the screw theory approach and its tools, like the Davies method and Assur virtual chains.

A novel parallel robot, dubbed the SDelta, is the subject of this paper. SDelta is a simpler alternative to both the well-known Stewart–Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base. This reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, which admits up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6 × 6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wr...

Joint-coupling (JC) is introduced in the design and control of parallel manipulators for managing manipulator singularities. The underlying idea consists of coupling the motions of several manipulator joints by driving the joints with a single actuator. This can be done by mechanical or electronic means, while preserving the mobility of the manipulator. Such JC is intended to alter the direct singularity condition of parallel manipulators upon changing the coupling coefficients. Both 2-and 3-d.o.f. planar parallel manipulator examples are provided to illustrate the concept of JC and singularity management. The prototype of a JC device and its associated 2-d.o.f. parallel manipulator intended for a feasibility study is introduced.

Rigid body displacement and motion parameterization is a research subject with continuous development in many theoretical and applied fields. A very important objective for the design of parameterization methods is to obtain a reduced number of algebraic equations and fewer variables for a more compact notation. This criterion increased the interest into tensorial based approaches for rigid motion parameterization. The present research analyzes the performance of tensorial parameterization and proposes new methods to compute the rigid-body motion parameters. Our rigid body motion parameterization solutions are developed using rigid bases of dual vectors, a new notion defined in this paper. Considering a rigid body motion, computational techniques are proposed for the orthogonal dual tensor, the screw parameters and the instantaneous screw parameters. The parameterization techniques proposed in this paper are described both algebraically and geometrically. Our solutions are sustained by the symbolic and numerical results gathered from Matlab implementations.

Dalam studi ini, dibahas kinematik forward dan kesalahan konstrain gerak dari mekanisme paralel 3-URU. Mekanisme ini disusun oleh platform, base dan tiga rantai kinematik dengan konfigurasi URU. Rantai kinematik ini terdiri dari tiga sumbu join sejajar dan dua sumbu join yang saling berpotongan. Arah sumbu dari join sejajar merupakan arah gaya konstrain yang bekerja pada titik pusat putar platform. Kesalahan pada sumbu join yang sejajar berpengaruh pada perpindahan titik pusat putar platform dan orientasi gerak platform. Kinematik forward dan kesalahan sumbu join sejajar merupakan masalah yang dibahas pada penelitian ini dalam rangka menghasilkan mekanisme paralel 3-URU dengan tingkat ketelitian gerak platform yang tinggi. Kinematik forward diterapkan dalam analisis perpindahan untuk mendapatkan hubungan pergerakan input dan output. Formulasi kinematik forward didapatkan secara analitis dan diselesaikan dengan menggunakan software Maple 16. Selanjutnya, kesalahan kesejajaran sumbu j...

A dimensional synthesis of parallel manipulators (PMs) consists of determining the values of the geometric parameters that affect the platform motion so that a useful workspace with assigned sizes can be suitably located in a free-from-singularity region of its operational space. The main goal of this preliminary dimensioning is to keep the PM far enough from singularities to avoid high internal loads in the links and guarantee a good positioning precision (i.e., for getting good kinematic performances). This paper presents a novel method for the dimensional synthesis of translational PMs (TPMs) and applies it to a TPM previously proposed by the author. The proposed method, which is based on Jacobians' properties, exploits the fact that TPM parallel Jacobians are block diagonal matrices to overcome typical drawbacks of indices based on Jacobian properties. The proposed method can be also applied to all the lower-mobility PMs with block diagonal Jacobians that separate platform rotations from platform translations (e.g., parallel wrists).

We prove, using the result of [5], that every 3-modal logic between K 3 and S5 3 is undecidable. We also show that each of these logics is non-finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. 1 Introduction and results Let L be any 3-modal logic with K 3 ` L ` S5 3 . Then the following hold. Theorem 1. L is undecidable. Theorem 2. It is undecidable whether a finite frame validates L. Theorem 3. L is not finitely axiomatizable. Theorem 4. L does not have the product finite model property in the following sense: there is some formula which does not belong to L but cannot be refuted in any finite product frame. Theorem 5. Theorems 1--4 also hold for any n-modal logic between K n and S5 n , if n 3. Theorems 1 and 3 answer questions 22 and 24 of Gabbay--Shehtman [2] (cf. also Q16.163 of Gabbay [1]): K 3 is undecidable, and all the logics of the form L Theta S5 2 are undecid...

Sunflower oil is extremely important and widely used in the food industry, pharmaceutics, cosmetology, and numerous technical fields. The main purpose of this research is to propose a novel design of a crew-type press for sunflower oil extraction and to analyze the stress-strain conditions of its certain components, particularly, connecting shaft and screw. Simulation results obtained in SolidWorks software show the distribution of equivalent stresses and deformations in the corresponding element.

This paper addresses the problem of characterizing a general class of cameras under reasonable, "linear" assumptions. Concretely, we use the formalism and terminology of classical projective geometry to model cameras by two-parameter linear families of straight lines-that is, degenerate reguli (rank-3 families) and non-degenerate linear congruences (rank-4 families). This model captures both the general linear cameras of Yu and McMillan [16] and the linear oblique cameras of Pajdla [8]. From a geometric perspective, it affords a simple classification of all possible camera configurations. From an analytical viewpoint, it also provides a simple and unified methodology for deriving general formulas for projection and inverse projection, triangulation, and binocular and trinocular geometry.

This special issue of the Mechanism and Machine Theory journal represents a modest tribute to a great personality, Professor Bernard ("Bernie") Roth, who on the 28th of May, 2018, celebrates his 85th birthday. Bernie is the Rodney H. Adams Professor of Engineering at Stanford University and co-founder of the Hasso Plattner Institute of Design at Stanford (known as the d.school). This special issue is both a recognition of his lifelong contributions to the science of mechanisms and robotics and a celebration of his birthday. We trust that the following introductory comments will serve as both a brief review of his academic career and his substantial influence in the fields of mechanisms, robotics, engineering creativity, and design thinking. As the guest editors we must begin by thanking the authors of the invited papers who contributed their time, their thoughts, and their research so generously by writing the articles for this commemorative issue. In inviting papers for this special issue, we thought it appropriate to emphasize, as much as possible, geographical diversity in keeping with the global nature of Bernie's sphere of influence. Due to the page limitation, we regret that we had to restrict the number of contributions, and were unable to invite so many outstanding researchers who would gladly have participated in this undertaking. The lead authors of the invited papers are Sunil K.

Sciatic nerve (SN) injuries after hip fracture dislocation are described and are not uncommon. Several factors can lead to SN injury after hip surgery; among other factors, screw plates of synthesis materials can immigrate and lead to nerve impingement. We report a case of a 22-year-old male with a history of posterior wall fracture and hip dislocation after a motorway accident. Ultrasonography showed massive swelling of the SN with a cross-sectional area measured at 1.50 cm 2 upstream to screw impingement. The reoperation option was judged too risky by the orthopedic surgeons; currently, the patient is undergoing platelet-rich plasma (PRP) injections around the nerve swelling and to the lifter muscles of the foot.

Compliant mechanisms perform precision movements generated by the elastic deformation of their flexible elements. For most applications, resonance frequencies must be bounded by a defined range of values. Therefore, a modal analysis of the mechanisms is required at the initial stage of design. In this work, a novel flexible platform with 2 degrees of rotational freedom restricted by beam-type flexure elements is analyzed. The Screw Theory description of the movement of the mechanism is used for the rigid and the flexible elements. Using this formalism, the stiffness and mass matrices for a two-node beam element are derived and can be assembled using a standard finite-element-like procedure to perform the modal analysis of the mechanism. Starting from the desired movements, the mechanism is synthesized using screws and a hybrid (series/parallel) solution is proposed. The analytical results for the modal analysis obtained by Screw Theory are compared with the results of finite element analysis. Due to the computational efficiency, the analytical equations are chosen to be applied in the optimization of the designs.

The design of flexible parallel stages has recently been systematised for the three-dimensional space using screw theory. The relationships between the twists (motions), the wrench actuations, and constraint wrenches spaces can be manipulated by linear algebra. The use of flexible beams to constraint small motions leads to simple precision mechanisms. In a previous work by the authors, an analytical enumeration of twists and their reciprocal wrenches for any degree of freedom with zero and infinite pitches was presented and validated using finite element analysis. This work extends the methodology to account for screws with finite non-null pitches. Two synthesis problems are analytically calculated and validated using finite element analysis.

This article discusses a generic synthesis methodology using the tools of screw theory and the concept of motion pattern, application of which is illustrated by the synthesis of novel parallel mechanisms suited to the task of needle manipulation derived from a medical application. From the minimal 2T2R mobility required for such task, two different motion patterns are derived and have permitted the synthesis of two novel 2T2R parallel mechanisms. Application of the kinematic inversion principle is demonstrated for special cases where the motion pattern is defined with respect to the moving platform. Throughout the synthesis process, a set of preference rules qualifying the architecture kinematic complexity is utilized in order to obtain parallel mechanisms with reduced complexity. These rules are related to the geometric conditions on the placement of the joint axes within and between the synthesized legs. Each parallel mechanism candidate is tested for conditions of full-cycle mobility. Finally, the selection of actuated joints is validated by analyzing the full direct Jacobian matrix.

Rigid body displacement and motion parameterization is a research subject with continuous development in many theoretical and applied fields. A very important objective for the design of parameterization methods is to obtain a reduced number of algebraic equations and fewer variables for a more compact notation. This criterion increased the interest into tensorial based approaches for rigid motion parameterization. The present research analyzes the performance of tensorial parameterization and proposes new methods to compute the rigid-body motion parameters. Our rigid body motion parameterization solutions are developed using rigid bases of dual vectors, a new notion defined in this paper. Considering a rigid body motion, computational techniques are proposed for the orthogonal dual tensor, the screw parameters and the instantaneous screw parameters. The parameterization techniques proposed in this paper are described both algebraically and geometrically. Our solutions are sustained by the symbolic and numerical results gathered from Matlab implementations.

Sciatic nerve (SN) injuries after hip fracture dislocation are described and are not uncommon. Several factors can lead to SN injury after hip surgery; among other factors, screw plates of synthesis materials can immigrate and lead to nerve impingement. We report a case of a 22-year-old male with a history of posterior wall fracture and hip dislocation after a motorway accident. Ultrasonography showed massive swelling of the SN with a cross-sectional area measured at 1.50 cm 2 upstream to screw impingement. The reoperation option was judged too risky by the orthopedic surgeons; currently, the patient is undergoing platelet-rich plasma (PRP) injections around the nerve swelling and to the lifter muscles of the foot.

Mesin manufaktur merupakan teknologi yang dapat membantu pekerjaan manusia. Salah satunya adalah cnc router 3018. Pada proses permesinan cnc router, tingkat kekasaran permukaan merupakan salah satu tolak ukur kualitas produk yang dihasilkan. Berangkat dari permasalahan ini diperlukan sebuah taktik dalam membuat variable parameter permesinan sehingga didapat nilai kekasaran permukaan yang baik. Bahan yang dipakai dalam penelitian ini adalah akrilik dengan ukuran 70 × 65 × 5 mm, dengan spindle speed konstan di 1000 rpm, feed rate bervariasi yaitu 200,300,400 mm/mnt dan deep of cut bervariasi yaitu 0.1,0.2,0.4 mm menggunakan pahat berbahan tungsten carbide satu flute dengan ukuran 3 mm. Dari Analisa yang telah dilakukan maka diperoleh nilai tingkat kekasaran (Ra) yang paling rendah didapat pada kondisi parameter : spindle speed 1000 rpm, dengan feed rate 400 mm/mnt dan deep of cut 0.1 mm dengan nilai 0.654. nilai (Ra) yang paling besar terdapat pada spindle speed 1000 rpm, dengan feed rate 300 dan deep of cut 0.4 mm dengan nilai (Ra) 1.740 , mengacu pada percobaan mengunakan variasi feed rate didapatkan bahwa pada hubungan feed rate dan nilai kekasaran bernilai negative dengan persamaan y =-0,001x + 1,3634 ini dapat menjadi acuan dalam menentukan nilai kekasaran permukaan.

This paper shows how the characteristic force capability polytope of a 3RRR parallel manipulator can be obtained from the optimization of its static equations. The objective function of the optimization problem of force capability is defined by employing the Screws Theory and Davies's method as a primary mathematical tool. In order to solve the problem regarding the global optimization, an evolutionary algorithm known as Differential Evolution (DE) is used. Finally, some force capability polytopes are obtained for different kinematic positions and different working modes of the manipulator.

Recently, industrial robots are being more and more widely used in a variety of machining applications, such as drilling, milling and grinding because of their flexibility in performing tasks in a relatively small space, and furthermore, at a lower cost. In many cases, the wrench capability of industrial robots is lower than the required, causing in some tasks the saturation of the actuators. The possibility of using two or more robots to perform a given task increases the wrench capability, allowing us to work out in applications which are impossible to solve using only one manipulator. A Cooperative Robotic System (CRS) increases the flexibility in the performance of tasks allowing a more homogeneous distribution of the forces generated during the interaction between the end-effector and the environment. In some cases, the CRS can be composed by robots with different capabilities, and a strategy for wrench distribution must be used. Recent works presented the force capability analysis using a scaling factor method for single serial robots. This paper proposes the use of this scaling factor method in CRS, seeking to obtain a balance of forces between the robots. The proposed method is discussed and graphical results are presented.

The interaction of a screw dislocation in a lamellar inclusion with multiple boundaries is investigated. An analytical solution is obtained for the force acting on the dislocation, and equilibrium positions are established for physically interesting special cases, such as a double layer bounded by free plane surfaces. A functional relationship is obtained which expresses the force on a screw dislocation on one side of an interface in terms of the force on a screw dislocation on the opposite side of the interface, thereby contributing to reduction of effort in the calculation process. c

This paper addresses the problem of identifying the parameters and the payloads of a 2-DOF robotic manipulator. The methodology proposed for our research was the algebraic identification method conducted in two stages: First, identifying the parameters of the manipulator and second, identifying the tip payload. Two different numerical simulation cases were used to validate the proposed identification methodology. In both cases, fast convergence was achieved with a low error percentage.

In this paper we present a technique for designing planar parallel manipulators with platforms capable of reaching any number of desired poses. The manipulator consists of a platform connected to ground by RPR chains. The set of positions and orientations available to the end-effector of a general RPR chain is mapped into the space of planar quaternions to obtain a quadratic manifold. The coefficients of this constraint manifold are functions of the locations of the base and platform R joints and the distance between them. Evaluating the constraint manifold at each desired pose and defining the limits on the extension of the P joint yields a set of equations. Solutions of these equations determine chains that contain the desired poses as part of their workspaces. Parallel manipulators that can reach the prescribed workspace are assembled from these chains. An example shows the determination of three RPR chains that form a manipulator able to reach a prescribed workspace.